Soliton fission from a large disturbance in the viscous fluid conduit system
The resolution of a large, localized initial disturbance is considered in the context of the viscous fluid conduit system--the driven, cylindrical, free interface between two miscible Stokes fluids with high viscosity contrast. Due to buoyancy induced nonlinear self-steepening balanced by stress induced interfacial dispersion, the disturbance evolves into a slowly modulated wavetrain. An extension of Whitham averaging theory termed solitary wave fitting is applied to find a relationship between the disturbance profile and the number of emergent solitary waves from the resultant wavetrain. The solitary wave amplitude distribution is also obtained. These predictions are confirmed both numerically and experimentally. The number of observed solitary waves is consistently within 1-2 waves of the prediction, and the amplitude distribution shows remarkable agreement. This is the first known experimental confirmation of this theory, and the method used is applicable to other dispersive hydrodynamic media.
Time permitting, a related problem will be explored for the Korteweg-deVries equation, in which the phase of a soliton after traveling through a disturbance is calculated.